A Bayes Formula for Nonlinear Filtering with Gaussian and Cox Noise. (3rd November 2011)

• Record Type: Journal Article
• Authors: Mandrekar, Vidyadhar; Meyer-Brandis, Thilo; Proske, Frank
• Other Names: Shepp L. A. Academic Editor.
• Is Part Of: Journal of probability and statistics. Volume 2011(2011)
• Publication Date: 2011-11-03
• Subjects: Probabilities -- Periodicals; Mathematical statistics -- Periodicals; Mathematical statistics; Probabilities; Periodicals; 519
• DOI: 10.1155/2011/259091
• Languages: English
• ISSNs: 1687-952X

Abstract

Abstract : A Bayes-type formula is derived for the nonlinear filter where the observation contains both general Gaussian noise as well as Cox noise whose jump intensity depends on the signal. This formula extends the well-known Kallianpur-Striebel formula in the classical non-linear filter setting. We also discuss Zakai-type equations for both the unnormalized conditional distribution as well as unnormalized conditional density in case the signal is a Markovian jump diffusion.